Properties

Label 48.3.l.a.19.8
Level $48$
Weight $3$
Character 48.19
Analytic conductor $1.308$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 48.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.30790526893\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.8
Root \(-1.96679 + 0.362960i\) of defining polynomial
Character \(\chi\) \(=\) 48.19
Dual form 48.3.l.a.43.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.96679 + 0.362960i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(3.73652 + 1.42773i) q^{4} +(1.69930 - 1.69930i) q^{5} +(-2.85335 + 1.96428i) q^{6} -5.74280 q^{7} +(6.83074 + 4.16426i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.96679 + 0.362960i) q^{2} +(-1.22474 + 1.22474i) q^{3} +(3.73652 + 1.42773i) q^{4} +(1.69930 - 1.69930i) q^{5} +(-2.85335 + 1.96428i) q^{6} -5.74280 q^{7} +(6.83074 + 4.16426i) q^{8} -3.00000i q^{9} +(3.95895 - 2.72539i) q^{10} +(-5.59560 - 5.59560i) q^{11} +(-6.32489 + 2.82768i) q^{12} +(-13.5782 - 13.5782i) q^{13} +(-11.2949 - 2.08441i) q^{14} +4.16243i q^{15} +(11.9232 + 10.6695i) q^{16} +19.7023 q^{17} +(1.08888 - 5.90037i) q^{18} +(-21.6943 + 21.6943i) q^{19} +(8.77563 - 3.92333i) q^{20} +(7.03347 - 7.03347i) q^{21} +(-8.97439 - 13.0363i) q^{22} +24.9257 q^{23} +(-13.4661 + 3.26576i) q^{24} +19.2247i q^{25} +(-21.7771 - 31.6337i) q^{26} +(3.67423 + 3.67423i) q^{27} +(-21.4581 - 8.19918i) q^{28} +(1.50581 + 1.50581i) q^{29} +(-1.51080 + 8.18662i) q^{30} -2.20037i q^{31} +(19.5777 + 25.3123i) q^{32} +13.7064 q^{33} +(38.7504 + 7.15116i) q^{34} +(-9.75877 + 9.75877i) q^{35} +(4.28320 - 11.2096i) q^{36} +(27.6956 - 27.6956i) q^{37} +(-50.5423 + 34.7940i) q^{38} +33.2596 q^{39} +(18.6838 - 4.53116i) q^{40} +51.3127i q^{41} +(16.3862 - 11.2805i) q^{42} +(21.4400 + 21.4400i) q^{43} +(-12.9191 - 28.8971i) q^{44} +(-5.09791 - 5.09791i) q^{45} +(49.0236 + 9.04703i) q^{46} -76.5216i q^{47} +(-27.6702 + 1.53542i) q^{48} -16.0202 q^{49} +(-6.97781 + 37.8110i) q^{50} +(-24.1303 + 24.1303i) q^{51} +(-31.3491 - 70.1211i) q^{52} +(-56.5145 + 56.5145i) q^{53} +(5.89284 + 8.56005i) q^{54} -19.0173 q^{55} +(-39.2276 - 23.9145i) q^{56} -53.1400i q^{57} +(2.41506 + 3.50816i) q^{58} +(-48.0041 - 48.0041i) q^{59} +(-5.94283 + 15.5530i) q^{60} +(-51.5587 - 51.5587i) q^{61} +(0.798646 - 4.32766i) q^{62} +17.2284i q^{63} +(29.3180 + 56.8899i) q^{64} -46.1469 q^{65} +(26.9575 + 4.97486i) q^{66} +(63.4445 - 63.4445i) q^{67} +(73.6182 + 28.1297i) q^{68} +(-30.5276 + 30.5276i) q^{69} +(-22.7355 + 15.6514i) q^{70} +43.4856 q^{71} +(12.4928 - 20.4922i) q^{72} +73.9992i q^{73} +(64.5239 - 44.4190i) q^{74} +(-23.5454 - 23.5454i) q^{75} +(-112.035 + 50.0876i) q^{76} +(32.1344 + 32.1344i) q^{77} +(65.4146 + 12.0719i) q^{78} -4.12659i q^{79} +(38.3918 - 2.13036i) q^{80} -9.00000 q^{81} +(-18.6245 + 100.921i) q^{82} +(38.4428 - 38.4428i) q^{83} +(36.3226 - 16.2388i) q^{84} +(33.4803 - 33.4803i) q^{85} +(34.3862 + 49.9499i) q^{86} -3.68846 q^{87} +(-14.9206 - 61.5236i) q^{88} -52.9839i q^{89} +(-8.17618 - 11.8769i) q^{90} +(77.9767 + 77.9767i) q^{91} +(93.1353 + 35.5872i) q^{92} +(2.69489 + 2.69489i) q^{93} +(27.7743 - 150.502i) q^{94} +73.7305i q^{95} +(-54.9788 - 7.02335i) q^{96} +23.1008 q^{97} +(-31.5084 - 5.81471i) q^{98} +(-16.7868 + 16.7868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 16q + 12q^{4} - 12q^{8} - 56q^{10} + 32q^{11} - 24q^{12} - 44q^{14} + 32q^{16} + 12q^{18} - 32q^{19} + 80q^{20} + 32q^{22} - 128q^{23} + 36q^{24} - 100q^{26} - 120q^{28} + 32q^{29} + 72q^{30} + 160q^{32} + 96q^{34} + 96q^{35} + 12q^{36} - 96q^{37} + 168q^{38} + 48q^{40} - 60q^{42} + 160q^{43} + 88q^{44} + 136q^{46} - 144q^{48} + 112q^{49} - 236q^{50} - 96q^{51} - 48q^{52} - 160q^{53} - 36q^{54} - 256q^{55} - 224q^{56} + 144q^{58} - 128q^{59} - 72q^{60} - 32q^{61} - 276q^{62} - 408q^{64} - 32q^{65} + 72q^{66} + 320q^{67} - 448q^{68} + 96q^{69} - 384q^{70} + 512q^{71} + 60q^{72} + 348q^{74} + 192q^{75} + 72q^{76} + 224q^{77} + 396q^{78} + 552q^{80} - 144q^{81} - 40q^{82} - 160q^{83} + 72q^{84} + 160q^{85} + 528q^{86} + 480q^{88} - 24q^{90} - 480q^{91} + 496q^{92} + 312q^{94} - 480q^{96} - 440q^{98} + 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.96679 + 0.362960i 0.983395 + 0.181480i
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 3.73652 + 1.42773i 0.934130 + 0.356933i
\(5\) 1.69930 1.69930i 0.339861 0.339861i −0.516454 0.856315i \(-0.672748\pi\)
0.856315 + 0.516454i \(0.172748\pi\)
\(6\) −2.85335 + 1.96428i −0.475558 + 0.327380i
\(7\) −5.74280 −0.820400 −0.410200 0.911996i \(-0.634541\pi\)
−0.410200 + 0.911996i \(0.634541\pi\)
\(8\) 6.83074 + 4.16426i 0.853842 + 0.520532i
\(9\) 3.00000i 0.333333i
\(10\) 3.95895 2.72539i 0.395895 0.272539i
\(11\) −5.59560 5.59560i −0.508691 0.508691i 0.405434 0.914125i \(-0.367121\pi\)
−0.914125 + 0.405434i \(0.867121\pi\)
\(12\) −6.32489 + 2.82768i −0.527074 + 0.235640i
\(13\) −13.5782 13.5782i −1.04447 1.04447i −0.998964 0.0455110i \(-0.985508\pi\)
−0.0455110 0.998964i \(-0.514492\pi\)
\(14\) −11.2949 2.08441i −0.806777 0.148886i
\(15\) 4.16243i 0.277495i
\(16\) 11.9232 + 10.6695i 0.745198 + 0.666844i
\(17\) 19.7023 1.15896 0.579481 0.814986i \(-0.303255\pi\)
0.579481 + 0.814986i \(0.303255\pi\)
\(18\) 1.08888 5.90037i 0.0604933 0.327798i
\(19\) −21.6943 + 21.6943i −1.14181 + 1.14181i −0.153687 + 0.988120i \(0.549115\pi\)
−0.988120 + 0.153687i \(0.950885\pi\)
\(20\) 8.77563 3.92333i 0.438782 0.196167i
\(21\) 7.03347 7.03347i 0.334927 0.334927i
\(22\) −8.97439 13.0363i −0.407927 0.592561i
\(23\) 24.9257 1.08373 0.541863 0.840467i \(-0.317719\pi\)
0.541863 + 0.840467i \(0.317719\pi\)
\(24\) −13.4661 + 3.26576i −0.561086 + 0.136073i
\(25\) 19.2247i 0.768989i
\(26\) −21.7771 31.6337i −0.837580 1.21668i
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −21.4581 8.19918i −0.766360 0.292828i
\(29\) 1.50581 + 1.50581i 0.0519245 + 0.0519245i 0.732592 0.680668i \(-0.238310\pi\)
−0.680668 + 0.732592i \(0.738310\pi\)
\(30\) −1.51080 + 8.18662i −0.0503598 + 0.272887i
\(31\) 2.20037i 0.0709796i −0.999370 0.0354898i \(-0.988701\pi\)
0.999370 0.0354898i \(-0.0112991\pi\)
\(32\) 19.5777 + 25.3123i 0.611805 + 0.791009i
\(33\) 13.7064 0.415344
\(34\) 38.7504 + 7.15116i 1.13972 + 0.210328i
\(35\) −9.75877 + 9.75877i −0.278822 + 0.278822i
\(36\) 4.28320 11.2096i 0.118978 0.311377i
\(37\) 27.6956 27.6956i 0.748530 0.748530i −0.225673 0.974203i \(-0.572458\pi\)
0.974203 + 0.225673i \(0.0724580\pi\)
\(38\) −50.5423 + 34.7940i −1.33006 + 0.915631i
\(39\) 33.2596 0.852810
\(40\) 18.6838 4.53116i 0.467096 0.113279i
\(41\) 51.3127i 1.25153i 0.780012 + 0.625764i \(0.215213\pi\)
−0.780012 + 0.625764i \(0.784787\pi\)
\(42\) 16.3862 11.2805i 0.390148 0.268583i
\(43\) 21.4400 + 21.4400i 0.498606 + 0.498606i 0.911004 0.412398i \(-0.135309\pi\)
−0.412398 + 0.911004i \(0.635309\pi\)
\(44\) −12.9191 28.8971i −0.293615 0.656752i
\(45\) −5.09791 5.09791i −0.113287 0.113287i
\(46\) 49.0236 + 9.04703i 1.06573 + 0.196675i
\(47\) 76.5216i 1.62812i −0.580781 0.814060i \(-0.697253\pi\)
0.580781 0.814060i \(-0.302747\pi\)
\(48\) −27.6702 + 1.53542i −0.576463 + 0.0319879i
\(49\) −16.0202 −0.326944
\(50\) −6.97781 + 37.8110i −0.139556 + 0.756220i
\(51\) −24.1303 + 24.1303i −0.473144 + 0.473144i
\(52\) −31.3491 70.1211i −0.602868 1.34848i
\(53\) −56.5145 + 56.5145i −1.06631 + 1.06631i −0.0686712 + 0.997639i \(0.521876\pi\)
−0.997639 + 0.0686712i \(0.978124\pi\)
\(54\) 5.89284 + 8.56005i 0.109127 + 0.158519i
\(55\) −19.0173 −0.345768
\(56\) −39.2276 23.9145i −0.700492 0.427044i
\(57\) 53.1400i 0.932281i
\(58\) 2.41506 + 3.50816i 0.0416390 + 0.0604855i
\(59\) −48.0041 48.0041i −0.813628 0.813628i 0.171547 0.985176i \(-0.445123\pi\)
−0.985176 + 0.171547i \(0.945123\pi\)
\(60\) −5.94283 + 15.5530i −0.0990472 + 0.259217i
\(61\) −51.5587 51.5587i −0.845224 0.845224i 0.144308 0.989533i \(-0.453904\pi\)
−0.989533 + 0.144308i \(0.953904\pi\)
\(62\) 0.798646 4.32766i 0.0128814 0.0698010i
\(63\) 17.2284i 0.273467i
\(64\) 29.3180 + 56.8899i 0.458093 + 0.888904i
\(65\) −46.1469 −0.709952
\(66\) 26.9575 + 4.97486i 0.408447 + 0.0753767i
\(67\) 63.4445 63.4445i 0.946934 0.946934i −0.0517277 0.998661i \(-0.516473\pi\)
0.998661 + 0.0517277i \(0.0164728\pi\)
\(68\) 73.6182 + 28.1297i 1.08262 + 0.413672i
\(69\) −30.5276 + 30.5276i −0.442429 + 0.442429i
\(70\) −22.7355 + 15.6514i −0.324793 + 0.223591i
\(71\) 43.4856 0.612473 0.306237 0.951955i \(-0.400930\pi\)
0.306237 + 0.951955i \(0.400930\pi\)
\(72\) 12.4928 20.4922i 0.173511 0.284614i
\(73\) 73.9992i 1.01369i 0.862038 + 0.506844i \(0.169188\pi\)
−0.862038 + 0.506844i \(0.830812\pi\)
\(74\) 64.5239 44.4190i 0.871944 0.600257i
\(75\) −23.5454 23.5454i −0.313939 0.313939i
\(76\) −112.035 + 50.0876i −1.47414 + 0.659047i
\(77\) 32.1344 + 32.1344i 0.417330 + 0.417330i
\(78\) 65.4146 + 12.0719i 0.838649 + 0.154768i
\(79\) 4.12659i 0.0522354i −0.999659 0.0261177i \(-0.991686\pi\)
0.999659 0.0261177i \(-0.00831446\pi\)
\(80\) 38.3918 2.13036i 0.479898 0.0266295i
\(81\) −9.00000 −0.111111
\(82\) −18.6245 + 100.921i −0.227127 + 1.23075i
\(83\) 38.4428 38.4428i 0.463166 0.463166i −0.436526 0.899692i \(-0.643791\pi\)
0.899692 + 0.436526i \(0.143791\pi\)
\(84\) 36.3226 16.2388i 0.432412 0.193319i
\(85\) 33.4803 33.4803i 0.393886 0.393886i
\(86\) 34.3862 + 49.9499i 0.399839 + 0.580813i
\(87\) −3.68846 −0.0423961
\(88\) −14.9206 61.5236i −0.169552 0.699132i
\(89\) 52.9839i 0.595325i −0.954671 0.297662i \(-0.903793\pi\)
0.954671 0.297662i \(-0.0962070\pi\)
\(90\) −8.17618 11.8769i −0.0908465 0.131965i
\(91\) 77.9767 + 77.9767i 0.856887 + 0.856887i
\(92\) 93.1353 + 35.5872i 1.01234 + 0.386817i
\(93\) 2.69489 + 2.69489i 0.0289773 + 0.0289773i
\(94\) 27.7743 150.502i 0.295471 1.60108i
\(95\) 73.7305i 0.776111i
\(96\) −54.9788 7.02335i −0.572696 0.0731599i
\(97\) 23.1008 0.238153 0.119077 0.992885i \(-0.462007\pi\)
0.119077 + 0.992885i \(0.462007\pi\)
\(98\) −31.5084 5.81471i −0.321515 0.0593337i
\(99\) −16.7868 + 16.7868i −0.169564 + 0.169564i
\(100\) −27.4478 + 71.8336i −0.274478 + 0.718336i
\(101\) 16.1216 16.1216i 0.159619 0.159619i −0.622779 0.782398i \(-0.713996\pi\)
0.782398 + 0.622779i \(0.213996\pi\)
\(102\) −56.2177 + 38.7010i −0.551153 + 0.379421i
\(103\) −98.8380 −0.959592 −0.479796 0.877380i \(-0.659289\pi\)
−0.479796 + 0.877380i \(0.659289\pi\)
\(104\) −36.2060 149.292i −0.348134 1.43550i
\(105\) 23.9040i 0.227657i
\(106\) −131.665 + 90.6395i −1.24212 + 0.855090i
\(107\) 15.6655 + 15.6655i 0.146406 + 0.146406i 0.776511 0.630104i \(-0.216988\pi\)
−0.630104 + 0.776511i \(0.716988\pi\)
\(108\) 8.48303 + 18.9747i 0.0785466 + 0.175691i
\(109\) 84.6938 + 84.6938i 0.777008 + 0.777008i 0.979321 0.202313i \(-0.0648459\pi\)
−0.202313 + 0.979321i \(0.564846\pi\)
\(110\) −37.4029 6.90250i −0.340027 0.0627500i
\(111\) 67.8401i 0.611172i
\(112\) −68.4724 61.2728i −0.611360 0.547079i
\(113\) 63.8537 0.565077 0.282538 0.959256i \(-0.408824\pi\)
0.282538 + 0.959256i \(0.408824\pi\)
\(114\) 19.2877 104.515i 0.169190 0.916800i
\(115\) 42.3563 42.3563i 0.368316 0.368316i
\(116\) 3.47659 + 7.77638i 0.0299706 + 0.0670377i
\(117\) −40.7345 + 40.7345i −0.348158 + 0.348158i
\(118\) −76.9903 111.837i −0.652461 0.947775i
\(119\) −113.147 −0.950812
\(120\) −17.3334 + 28.4325i −0.144445 + 0.236937i
\(121\) 58.3785i 0.482467i
\(122\) −82.6913 120.119i −0.677798 0.984580i
\(123\) −62.8449 62.8449i −0.510934 0.510934i
\(124\) 3.14154 8.22172i 0.0253350 0.0663042i
\(125\) 75.1513 + 75.1513i 0.601210 + 0.601210i
\(126\) −6.25322 + 33.8846i −0.0496288 + 0.268926i
\(127\) 36.8901i 0.290473i 0.989397 + 0.145237i \(0.0463944\pi\)
−0.989397 + 0.145237i \(0.953606\pi\)
\(128\) 37.0135 + 122.532i 0.289168 + 0.957278i
\(129\) −52.5172 −0.407110
\(130\) −90.7612 16.7495i −0.698163 0.128842i
\(131\) −40.4136 + 40.4136i −0.308500 + 0.308500i −0.844328 0.535827i \(-0.820000\pi\)
0.535827 + 0.844328i \(0.320000\pi\)
\(132\) 51.2141 + 19.5690i 0.387986 + 0.148250i
\(133\) 124.586 124.586i 0.936738 0.936738i
\(134\) 147.810 101.754i 1.10306 0.759360i
\(135\) 12.4873 0.0924984
\(136\) 134.582 + 82.0456i 0.989570 + 0.603276i
\(137\) 253.499i 1.85036i −0.379531 0.925179i \(-0.623915\pi\)
0.379531 0.925179i \(-0.376085\pi\)
\(138\) −71.1217 + 48.9611i −0.515375 + 0.354790i
\(139\) 67.8065 + 67.8065i 0.487816 + 0.487816i 0.907617 0.419800i \(-0.137900\pi\)
−0.419800 + 0.907617i \(0.637900\pi\)
\(140\) −50.3967 + 22.5309i −0.359977 + 0.160935i
\(141\) 93.7194 + 93.7194i 0.664677 + 0.664677i
\(142\) 85.5270 + 15.7835i 0.602303 + 0.111152i
\(143\) 151.956i 1.06263i
\(144\) 32.0085 35.7695i 0.222281 0.248399i
\(145\) 5.11766 0.0352942
\(146\) −26.8588 + 145.541i −0.183964 + 0.996856i
\(147\) 19.6207 19.6207i 0.133474 0.133474i
\(148\) 143.027 63.9433i 0.966400 0.432049i
\(149\) −43.9337 + 43.9337i −0.294857 + 0.294857i −0.838996 0.544138i \(-0.816857\pi\)
0.544138 + 0.838996i \(0.316857\pi\)
\(150\) −37.7628 54.8549i −0.251752 0.365699i
\(151\) −223.084 −1.47738 −0.738688 0.674047i \(-0.764554\pi\)
−0.738688 + 0.674047i \(0.764554\pi\)
\(152\) −238.529 + 57.8475i −1.56927 + 0.380576i
\(153\) 59.1070i 0.386320i
\(154\) 51.5381 + 74.8651i 0.334663 + 0.486137i
\(155\) −3.73909 3.73909i −0.0241232 0.0241232i
\(156\) 124.275 + 47.4858i 0.796636 + 0.304396i
\(157\) −78.8526 78.8526i −0.502246 0.502246i 0.409889 0.912135i \(-0.365567\pi\)
−0.912135 + 0.409889i \(0.865567\pi\)
\(158\) 1.49779 8.11614i 0.00947968 0.0513680i
\(159\) 138.432i 0.870639i
\(160\) 76.2818 + 9.74473i 0.476761 + 0.0609045i
\(161\) −143.143 −0.889089
\(162\) −17.7011 3.26664i −0.109266 0.0201644i
\(163\) 52.2425 52.2425i 0.320506 0.320506i −0.528455 0.848961i \(-0.677228\pi\)
0.848961 + 0.528455i \(0.177228\pi\)
\(164\) −73.2607 + 191.731i −0.446712 + 1.16909i
\(165\) 23.2913 23.2913i 0.141159 0.141159i
\(166\) 89.5620 61.6556i 0.539530 0.371419i
\(167\) 96.5201 0.577965 0.288982 0.957334i \(-0.406683\pi\)
0.288982 + 0.957334i \(0.406683\pi\)
\(168\) 77.3329 18.7546i 0.460315 0.111635i
\(169\) 199.734i 1.18186i
\(170\) 78.0006 53.6966i 0.458827 0.315863i
\(171\) 65.0830 + 65.0830i 0.380602 + 0.380602i
\(172\) 49.5005 + 110.722i 0.287794 + 0.643731i
\(173\) −46.3076 46.3076i −0.267674 0.267674i 0.560488 0.828162i \(-0.310614\pi\)
−0.828162 + 0.560488i \(0.810614\pi\)
\(174\) −7.25443 1.33877i −0.0416921 0.00769405i
\(175\) 110.404i 0.630879i
\(176\) −7.01501 126.419i −0.0398580 0.718293i
\(177\) 117.585 0.664325
\(178\) 19.2310 104.208i 0.108040 0.585439i
\(179\) −93.5440 + 93.5440i −0.522592 + 0.522592i −0.918353 0.395761i \(-0.870481\pi\)
0.395761 + 0.918353i \(0.370481\pi\)
\(180\) −11.7700 26.3269i −0.0653889 0.146261i
\(181\) −115.810 + 115.810i −0.639836 + 0.639836i −0.950515 0.310679i \(-0.899444\pi\)
0.310679 + 0.950515i \(0.399444\pi\)
\(182\) 125.061 + 181.666i 0.687150 + 0.998166i
\(183\) 126.292 0.690123
\(184\) 170.261 + 103.797i 0.925331 + 0.564114i
\(185\) 94.1266i 0.508792i
\(186\) 4.32214 + 6.27842i 0.0232373 + 0.0337549i
\(187\) −110.246 110.246i −0.589553 0.589553i
\(188\) 109.252 285.925i 0.581130 1.52088i
\(189\) −21.1004 21.1004i −0.111642 0.111642i
\(190\) −26.7612 + 145.012i −0.140849 + 0.763223i
\(191\) 35.2964i 0.184798i 0.995722 + 0.0923991i \(0.0294535\pi\)
−0.995722 + 0.0923991i \(0.970546\pi\)
\(192\) −105.583 33.7686i −0.549909 0.175878i
\(193\) −364.339 −1.88777 −0.943884 0.330277i \(-0.892858\pi\)
−0.943884 + 0.330277i \(0.892858\pi\)
\(194\) 45.4345 + 8.38468i 0.234198 + 0.0432200i
\(195\) 56.5182 56.5182i 0.289837 0.289837i
\(196\) −59.8599 22.8726i −0.305408 0.116697i
\(197\) 130.582 130.582i 0.662851 0.662851i −0.293200 0.956051i \(-0.594720\pi\)
0.956051 + 0.293200i \(0.0947203\pi\)
\(198\) −39.1090 + 26.9232i −0.197520 + 0.135976i
\(199\) −12.7493 −0.0640670 −0.0320335 0.999487i \(-0.510198\pi\)
−0.0320335 + 0.999487i \(0.510198\pi\)
\(200\) −80.0567 + 131.319i −0.400283 + 0.656595i
\(201\) 155.407i 0.773168i
\(202\) 37.5592 25.8562i 0.185937 0.128001i
\(203\) −8.64756 8.64756i −0.0425988 0.0425988i
\(204\) −124.615 + 55.7119i −0.610859 + 0.273097i
\(205\) 87.1958 + 87.1958i 0.425346 + 0.425346i
\(206\) −194.394 35.8743i −0.943658 0.174147i
\(207\) 74.7771i 0.361242i
\(208\) −17.0225 306.767i −0.0818388 1.47484i
\(209\) 242.786 1.16165
\(210\) 8.67620 47.0141i 0.0413152 0.223877i
\(211\) 8.59499 8.59499i 0.0407345 0.0407345i −0.686446 0.727181i \(-0.740830\pi\)
0.727181 + 0.686446i \(0.240830\pi\)
\(212\) −291.855 + 130.480i −1.37667 + 0.615471i
\(213\) −53.2588 + 53.2588i −0.250041 + 0.250041i
\(214\) 25.1247 + 36.4966i 0.117405 + 0.170545i
\(215\) 72.8663 0.338913
\(216\) 9.79728 + 40.3982i 0.0453578 + 0.187029i
\(217\) 12.6363i 0.0582317i
\(218\) 135.834 + 197.315i 0.623094 + 0.905117i
\(219\) −90.6302 90.6302i −0.413837 0.413837i
\(220\) −71.0583 27.1515i −0.322992 0.123416i
\(221\) −267.522 267.522i −1.21051 1.21051i
\(222\) −24.6233 + 133.427i −0.110916 + 0.601024i
\(223\) 50.5909i 0.226865i −0.993546 0.113433i \(-0.963815\pi\)
0.993546 0.113433i \(-0.0361846\pi\)
\(224\) −112.431 145.363i −0.501925 0.648944i
\(225\) 57.6742 0.256330
\(226\) 125.587 + 23.1763i 0.555693 + 0.102550i
\(227\) 31.7175 31.7175i 0.139725 0.139725i −0.633785 0.773509i \(-0.718499\pi\)
0.773509 + 0.633785i \(0.218499\pi\)
\(228\) 75.8697 198.559i 0.332762 0.870872i
\(229\) −169.826 + 169.826i −0.741599 + 0.741599i −0.972886 0.231287i \(-0.925706\pi\)
0.231287 + 0.972886i \(0.425706\pi\)
\(230\) 98.6796 67.9323i 0.429042 0.295358i
\(231\) −78.7129 −0.340749
\(232\) 4.01521 + 16.5564i 0.0173070 + 0.0713636i
\(233\) 363.082i 1.55829i 0.626844 + 0.779145i \(0.284346\pi\)
−0.626844 + 0.779145i \(0.715654\pi\)
\(234\) −94.9012 + 65.3312i −0.405561 + 0.279193i
\(235\) −130.033 130.033i −0.553334 0.553334i
\(236\) −110.831 247.905i −0.469624 1.05045i
\(237\) 5.05402 + 5.05402i 0.0213250 + 0.0213250i
\(238\) −222.536 41.0677i −0.935024 0.172553i
\(239\) 27.6282i 0.115599i −0.998328 0.0577996i \(-0.981592\pi\)
0.998328 0.0577996i \(-0.0184084\pi\)
\(240\) −44.4110 + 49.6293i −0.185046 + 0.206789i
\(241\) 368.121 1.52747 0.763737 0.645527i \(-0.223362\pi\)
0.763737 + 0.645527i \(0.223362\pi\)
\(242\) 21.1891 114.818i 0.0875581 0.474456i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) −119.038 266.262i −0.487861 1.09124i
\(245\) −27.2233 + 27.2233i −0.111115 + 0.111115i
\(246\) −100.793 146.413i −0.409726 0.595175i
\(247\) 589.139 2.38518
\(248\) 9.16290 15.0301i 0.0369472 0.0606054i
\(249\) 94.1651i 0.378173i
\(250\) 120.530 + 175.084i 0.482119 + 0.700334i
\(251\) 329.839 + 329.839i 1.31410 + 1.31410i 0.918365 + 0.395734i \(0.129510\pi\)
0.395734 + 0.918365i \(0.370490\pi\)
\(252\) −24.5975 + 64.3743i −0.0976093 + 0.255453i
\(253\) −139.474 139.474i −0.551281 0.551281i
\(254\) −13.3896 + 72.5551i −0.0527151 + 0.285650i
\(255\) 82.0096i 0.321606i
\(256\) 28.3236 + 254.428i 0.110639 + 0.993861i
\(257\) 23.6762 0.0921252 0.0460626 0.998939i \(-0.485333\pi\)
0.0460626 + 0.998939i \(0.485333\pi\)
\(258\) −103.290 19.0616i −0.400350 0.0738823i
\(259\) −159.050 + 159.050i −0.614094 + 0.614094i
\(260\) −172.429 65.8854i −0.663188 0.253405i
\(261\) 4.51743 4.51743i 0.0173082 0.0173082i
\(262\) −94.1535 + 64.8164i −0.359364 + 0.247391i
\(263\) 243.854 0.927202 0.463601 0.886044i \(-0.346557\pi\)
0.463601 + 0.886044i \(0.346557\pi\)
\(264\) 93.6246 + 57.0768i 0.354639 + 0.216200i
\(265\) 192.071i 0.724794i
\(266\) 290.255 199.815i 1.09118 0.751184i
\(267\) 64.8918 + 64.8918i 0.243040 + 0.243040i
\(268\) 327.644 146.480i 1.22255 0.546567i
\(269\) 234.293 + 234.293i 0.870976 + 0.870976i 0.992579 0.121603i \(-0.0388035\pi\)
−0.121603 + 0.992579i \(0.538803\pi\)
\(270\) 24.5599 + 4.53239i 0.0909624 + 0.0167866i
\(271\) 30.9533i 0.114219i −0.998368 0.0571094i \(-0.981812\pi\)
0.998368 0.0571094i \(-0.0181884\pi\)
\(272\) 234.914 + 210.214i 0.863655 + 0.772846i
\(273\) −191.003 −0.699646
\(274\) 92.0100 498.579i 0.335803 1.81963i
\(275\) 107.574 107.574i 0.391178 0.391178i
\(276\) −157.652 + 70.4818i −0.571204 + 0.255369i
\(277\) −41.4479 + 41.4479i −0.149631 + 0.149631i −0.777953 0.628322i \(-0.783742\pi\)
0.628322 + 0.777953i \(0.283742\pi\)
\(278\) 108.750 + 157.972i 0.391187 + 0.568245i
\(279\) −6.60110 −0.0236599
\(280\) −107.298 + 26.0216i −0.383206 + 0.0929342i
\(281\) 93.3971i 0.332374i −0.986094 0.166187i \(-0.946854\pi\)
0.986094 0.166187i \(-0.0531455\pi\)
\(282\) 150.310 + 218.343i 0.533014 + 0.774265i
\(283\) 40.0982 + 40.0982i 0.141690 + 0.141690i 0.774394 0.632704i \(-0.218055\pi\)
−0.632704 + 0.774394i \(0.718055\pi\)
\(284\) 162.485 + 62.0858i 0.572130 + 0.218612i
\(285\) −90.3011 90.3011i −0.316846 0.316846i
\(286\) −55.1540 + 298.866i −0.192846 + 1.04498i
\(287\) 294.678i 1.02675i
\(288\) 75.9369 58.7332i 0.263670 0.203935i
\(289\) 99.1824 0.343192
\(290\) 10.0654 + 1.85750i 0.0347081 + 0.00640519i
\(291\) −28.2926 + 28.2926i −0.0972256 + 0.0972256i
\(292\) −105.651 + 276.500i −0.361819 + 0.946917i
\(293\) 141.326 141.326i 0.482340 0.482340i −0.423538 0.905878i \(-0.639212\pi\)
0.905878 + 0.423538i \(0.139212\pi\)
\(294\) 45.7113 31.4683i 0.155481 0.107035i
\(295\) −163.147 −0.553041
\(296\) 304.513 73.8499i 1.02876 0.249493i
\(297\) 41.1191i 0.138448i
\(298\) −102.355 + 70.4622i −0.343472 + 0.236450i
\(299\) −338.445 338.445i −1.13192 1.13192i
\(300\) −54.3613 121.594i −0.181204 0.405314i
\(301\) −123.126 123.126i −0.409056 0.409056i
\(302\) −438.759 80.9705i −1.45284 0.268114i
\(303\) 39.4896i 0.130329i
\(304\) −490.133 + 27.1974i −1.61228 + 0.0894652i
\(305\) −175.228 −0.574517
\(306\) 21.4535 116.251i 0.0701095 0.379905i
\(307\) −285.548 + 285.548i −0.930125 + 0.930125i −0.997713 0.0675885i \(-0.978470\pi\)
0.0675885 + 0.997713i \(0.478470\pi\)
\(308\) 74.1916 + 165.950i 0.240882 + 0.538799i
\(309\) 121.051 121.051i 0.391752 0.391752i
\(310\) −5.99687 8.71115i −0.0193447 0.0281005i
\(311\) −365.454 −1.17509 −0.587547 0.809190i \(-0.699906\pi\)
−0.587547 + 0.809190i \(0.699906\pi\)
\(312\) 227.188 + 138.501i 0.728165 + 0.443915i
\(313\) 461.508i 1.47447i −0.675638 0.737234i \(-0.736132\pi\)
0.675638 0.737234i \(-0.263868\pi\)
\(314\) −126.466 183.707i −0.402758 0.585054i
\(315\) 29.2763 + 29.2763i 0.0929406 + 0.0929406i
\(316\) 5.89167 15.4191i 0.0186445 0.0487946i
\(317\) −319.216 319.216i −1.00699 1.00699i −0.999975 0.00701388i \(-0.997767\pi\)
−0.00701388 0.999975i \(-0.502233\pi\)
\(318\) 50.2451 272.266i 0.158004 0.856182i
\(319\) 16.8518i 0.0528270i
\(320\) 146.493 + 46.8531i 0.457792 + 0.146416i
\(321\) −38.3724 −0.119540
\(322\) −281.533 51.9553i −0.874325 0.161352i
\(323\) −427.429 + 427.429i −1.32331 + 1.32331i
\(324\) −33.6287 12.8496i −0.103792 0.0396592i
\(325\) 261.037 261.037i 0.803190 0.803190i
\(326\) 121.712 83.7881i 0.373350 0.257019i
\(327\) −207.457 −0.634424
\(328\) −213.679 + 350.503i −0.651461 + 1.06861i
\(329\) 439.448i 1.33571i
\(330\) 54.2629 37.3552i 0.164433 0.113198i
\(331\) −85.7864 85.7864i −0.259173 0.259173i 0.565544 0.824718i \(-0.308666\pi\)
−0.824718 + 0.565544i \(0.808666\pi\)
\(332\) 198.528 88.7562i 0.597976 0.267338i
\(333\) −83.0869 83.0869i −0.249510 0.249510i
\(334\) 189.835 + 35.0329i 0.568367 + 0.104889i
\(335\) 215.623i 0.643651i
\(336\) 158.905 8.81761i 0.472931 0.0262429i
\(337\) 258.256 0.766339 0.383170 0.923678i \(-0.374832\pi\)
0.383170 + 0.923678i \(0.374832\pi\)
\(338\) −72.4953 + 392.834i −0.214483 + 1.16223i
\(339\) −78.2045 + 78.2045i −0.230692 + 0.230692i
\(340\) 172.901 77.2989i 0.508531 0.227350i
\(341\) −12.3124 + 12.3124i −0.0361067 + 0.0361067i
\(342\) 104.382 + 151.627i 0.305210 + 0.443354i
\(343\) 373.398 1.08862
\(344\) 57.1695 + 235.733i 0.166190 + 0.685271i
\(345\) 103.751i 0.300729i
\(346\) −74.2695 107.885i −0.214652 0.311807i
\(347\) 27.7237 + 27.7237i 0.0798953 + 0.0798953i 0.745925 0.666030i \(-0.232008\pi\)
−0.666030 + 0.745925i \(0.732008\pi\)
\(348\) −13.7820 5.26614i −0.0396035 0.0151326i
\(349\) 321.089 + 321.089i 0.920027 + 0.920027i 0.997031 0.0770037i \(-0.0245353\pi\)
−0.0770037 + 0.997031i \(0.524535\pi\)
\(350\) 40.0722 217.141i 0.114492 0.620403i
\(351\) 99.7788i 0.284270i
\(352\) 32.0882 251.187i 0.0911596 0.713599i
\(353\) −241.363 −0.683748 −0.341874 0.939746i \(-0.611062\pi\)
−0.341874 + 0.939746i \(0.611062\pi\)
\(354\) 231.266 + 42.6788i 0.653293 + 0.120562i
\(355\) 73.8953 73.8953i 0.208156 0.208156i
\(356\) 75.6468 197.975i 0.212491 0.556111i
\(357\) 138.576 138.576i 0.388167 0.388167i
\(358\) −217.934 + 150.029i −0.608754 + 0.419074i
\(359\) −363.821 −1.01343 −0.506714 0.862114i \(-0.669140\pi\)
−0.506714 + 0.862114i \(0.669140\pi\)
\(360\) −13.5935 56.0515i −0.0377597 0.155699i
\(361\) 580.287i 1.60744i
\(362\) −269.809 + 185.740i −0.745329 + 0.513094i
\(363\) 71.4988 + 71.4988i 0.196966 + 0.196966i
\(364\) 180.032 + 402.692i 0.494593 + 1.10630i
\(365\) 125.747 + 125.747i 0.344513 + 0.344513i
\(366\) 248.391 + 45.8391i 0.678663 + 0.125244i
\(367\) 411.402i 1.12099i 0.828159 + 0.560493i \(0.189388\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(368\) 297.193 + 265.945i 0.807590 + 0.722676i
\(369\) 153.938 0.417176
\(370\) 34.1642 185.127i 0.0923356 0.500344i
\(371\) 324.551 324.551i 0.874801 0.874801i
\(372\) 6.22193 + 13.9171i 0.0167256 + 0.0374115i
\(373\) −225.677 + 225.677i −0.605033 + 0.605033i −0.941644 0.336611i \(-0.890719\pi\)
0.336611 + 0.941644i \(0.390719\pi\)
\(374\) −176.816 256.847i −0.472771 0.686756i
\(375\) −184.082 −0.490886
\(376\) 318.656 522.699i 0.847488 1.39016i
\(377\) 40.8923i 0.108468i
\(378\) −33.8414 49.1586i −0.0895276 0.130049i
\(379\) −157.180 157.180i −0.414724 0.414724i 0.468656 0.883381i \(-0.344738\pi\)
−0.883381 + 0.468656i \(0.844738\pi\)
\(380\) −105.267 + 275.496i −0.277019 + 0.724988i
\(381\) −45.1810 45.1810i −0.118585 0.118585i
\(382\) −12.8112 + 69.4207i −0.0335372 + 0.181729i
\(383\) 703.356i 1.83644i 0.396072 + 0.918219i \(0.370373\pi\)
−0.396072 + 0.918219i \(0.629627\pi\)
\(384\) −195.402 104.738i −0.508860 0.272755i
\(385\) 109.212 0.283668
\(386\) −716.578 132.241i −1.85642 0.342592i
\(387\) 64.3201 64.3201i 0.166202 0.166202i
\(388\) 86.3168 + 32.9818i 0.222466 + 0.0850047i
\(389\) 10.7401 10.7401i 0.0276095 0.0276095i −0.693167 0.720777i \(-0.743785\pi\)
0.720777 + 0.693167i \(0.243785\pi\)
\(390\) 131.673 90.6455i 0.337623 0.232424i
\(391\) 491.095 1.25600
\(392\) −109.430 66.7124i −0.279158 0.170185i
\(393\) 98.9926i 0.251890i
\(394\) 304.222 209.431i 0.772138 0.531550i
\(395\) −7.01234 7.01234i −0.0177528 0.0177528i
\(396\) −86.6913 + 38.7572i −0.218917 + 0.0978716i
\(397\) 365.020 + 365.020i 0.919446 + 0.919446i 0.996989 0.0775433i \(-0.0247076\pi\)
−0.0775433 + 0.996989i \(0.524708\pi\)
\(398\) −25.0753 4.62750i −0.0630032 0.0116269i
\(399\) 305.173i 0.764844i
\(400\) −205.118 + 229.220i −0.512796 + 0.573049i
\(401\) 341.735 0.852207 0.426104 0.904674i \(-0.359886\pi\)
0.426104 + 0.904674i \(0.359886\pi\)
\(402\) −56.4065 + 305.652i −0.140315 + 0.760329i
\(403\) −29.8770 + 29.8770i −0.0741364 + 0.0741364i
\(404\) 83.2558 37.2213i 0.206079 0.0921318i
\(405\) −15.2937 + 15.2937i −0.0377623 + 0.0377623i
\(406\) −13.8692 20.1467i −0.0341606 0.0496223i
\(407\) −309.947 −0.761541
\(408\) −265.313 + 64.3431i −0.650277 + 0.157704i
\(409\) 368.259i 0.900389i −0.892931 0.450194i \(-0.851355\pi\)
0.892931 0.450194i \(-0.148645\pi\)
\(410\) 139.847 + 203.144i 0.341091 + 0.495474i
\(411\) 310.472 + 310.472i 0.755405 + 0.755405i
\(412\) −369.310 141.114i −0.896384 0.342510i
\(413\) 275.678 + 275.678i 0.667501 + 0.667501i
\(414\) 27.1411 147.071i 0.0655582 0.355243i
\(415\) 130.652i 0.314824i
\(416\) 77.8646 609.525i 0.187174 1.46520i
\(417\) −166.091 −0.398300
\(418\) 477.508 + 88.1215i 1.14236 + 0.210817i
\(419\) 407.140 407.140i 0.971694 0.971694i −0.0279165 0.999610i \(-0.508887\pi\)
0.999610 + 0.0279165i \(0.00888725\pi\)
\(420\) 34.1285 89.3178i 0.0812583 0.212661i
\(421\) 57.5576 57.5576i 0.136716 0.136716i −0.635437 0.772153i \(-0.719180\pi\)
0.772153 + 0.635437i \(0.219180\pi\)
\(422\) 20.0242 13.7849i 0.0474506 0.0326656i
\(423\) −229.565 −0.542706
\(424\) −621.376 + 150.695i −1.46551 + 0.355412i
\(425\) 378.772i 0.891229i
\(426\) −124.080 + 85.4180i −0.291267 + 0.200512i
\(427\) 296.091 + 296.091i 0.693422 + 0.693422i
\(428\) 36.1683 + 80.9005i 0.0845053 + 0.189020i
\(429\) −186.107 186.107i −0.433817 0.433817i
\(430\) 143.313 + 26.4476i 0.333285 + 0.0615060i
\(431\) 796.565i 1.84818i −0.382177 0.924089i \(-0.624826\pi\)
0.382177 0.924089i \(-0.375174\pi\)
\(432\) 4.60626 + 83.0107i 0.0106626 + 0.192154i
\(433\) −335.804 −0.775529 −0.387764 0.921758i \(-0.626753\pi\)
−0.387764 + 0.921758i \(0.626753\pi\)
\(434\) −4.58646 + 24.8529i −0.0105679 + 0.0572647i
\(435\) −6.26782 + 6.26782i −0.0144088 + 0.0144088i
\(436\) 195.540 + 437.380i 0.448487 + 1.00317i
\(437\) −540.746 + 540.746i −1.23741 + 1.23741i
\(438\) −145.355 211.146i −0.331862 0.482068i
\(439\) −285.630 −0.650638 −0.325319 0.945604i \(-0.605472\pi\)
−0.325319 + 0.945604i \(0.605472\pi\)
\(440\) −129.902 79.1927i −0.295232 0.179983i
\(441\) 48.0607i 0.108981i
\(442\) −429.059 623.259i −0.970722 1.41009i
\(443\) 111.596 + 111.596i 0.251909 + 0.251909i 0.821753 0.569844i \(-0.192996\pi\)
−0.569844 + 0.821753i \(0.692996\pi\)
\(444\) −96.8575 + 253.486i −0.218148 + 0.570914i
\(445\) −90.0358 90.0358i −0.202328 0.202328i
\(446\) 18.3625 99.5017i 0.0411715 0.223098i
\(447\) 107.615i 0.240750i
\(448\) −168.367 326.707i −0.375820 0.729257i
\(449\) −99.6741 −0.221991 −0.110996 0.993821i \(-0.535404\pi\)
−0.110996 + 0.993821i \(0.535404\pi\)
\(450\) 113.433 + 20.9334i 0.252073 + 0.0465187i
\(451\) 287.125 287.125i 0.636641 0.636641i
\(452\) 238.591 + 91.1659i 0.527855 + 0.201695i
\(453\) 273.221 273.221i 0.603137 0.603137i
\(454\) 73.8939 50.8695i 0.162762 0.112047i
\(455\) 265.012 0.582445
\(456\) 221.289 362.986i 0.485282 0.796021i
\(457\) 32.1643i 0.0703813i 0.999381 + 0.0351907i \(0.0112039\pi\)
−0.999381 + 0.0351907i \(0.988796\pi\)
\(458\) −395.652 + 272.372i −0.863870 + 0.594699i
\(459\) 72.3910 + 72.3910i 0.157715 + 0.157715i
\(460\) 218.739 97.7918i 0.475519 0.212591i
\(461\) 165.361 + 165.361i 0.358701 + 0.358701i 0.863334 0.504633i \(-0.168372\pi\)
−0.504633 + 0.863334i \(0.668372\pi\)
\(462\) −154.812 28.5697i −0.335090 0.0618391i
\(463\) 923.215i 1.99398i 0.0774991 + 0.996992i \(0.475307\pi\)
−0.0774991 + 0.996992i \(0.524693\pi\)
\(464\) 1.88778 + 34.0202i 0.00406849 + 0.0733195i
\(465\) 9.15887 0.0196965
\(466\) −131.784 + 714.105i −0.282798 + 1.53241i
\(467\) 507.842 507.842i 1.08746 1.08746i 0.0916660 0.995790i \(-0.470781\pi\)
0.995790 0.0916660i \(-0.0292192\pi\)
\(468\) −210.363 + 94.0474i −0.449494 + 0.200956i
\(469\) −364.349 + 364.349i −0.776864 + 0.776864i
\(470\) −208.551 302.945i −0.443727 0.644565i
\(471\) 193.149 0.410082
\(472\) −128.002 527.805i −0.271191 1.11823i
\(473\) 239.940i 0.507272i
\(474\) 8.10579 + 11.7746i 0.0171008 + 0.0248409i
\(475\) −417.068 417.068i −0.878037 0.878037i
\(476\) −422.775 161.543i −0.888182 0.339376i
\(477\) 169.543 + 169.543i 0.355437 + 0.355437i
\(478\) 10.0279 54.3389i 0.0209789 0.113680i
\(479\) 52.3866i 0.109367i −0.998504 0.0546833i \(-0.982585\pi\)
0.998504 0.0546833i \(-0.0174149\pi\)
\(480\) −105.361 + 81.4910i −0.219501 + 0.169773i
\(481\) −752.112 −1.56364
\(482\) 724.017 + 133.613i 1.50211 + 0.277206i
\(483\) 175.314 175.314i 0.362969 0.362969i
\(484\) 83.3489 218.132i 0.172208 0.450687i
\(485\) 39.2554 39.2554i 0.0809389 0.0809389i
\(486\) 25.6801 17.6785i 0.0528398 0.0363756i
\(487\) −715.733 −1.46968 −0.734839 0.678241i \(-0.762742\pi\)
−0.734839 + 0.678241i \(0.762742\pi\)
\(488\) −137.480 566.887i −0.281722 1.16165i
\(489\) 127.968i 0.261692i
\(490\) −63.4234 + 43.6614i −0.129435 + 0.0891050i
\(491\) −22.3258 22.3258i −0.0454701 0.0454701i 0.684006 0.729476i \(-0.260236\pi\)
−0.729476 + 0.684006i \(0.760236\pi\)
\(492\) −145.096 324.547i −0.294910 0.659649i
\(493\) 29.6680 + 29.6680i 0.0601784 + 0.0601784i
\(494\) 1158.71 + 213.834i 2.34557 + 0.432862i
\(495\) 57.0518i 0.115256i
\(496\) 23.4768 26.2353i 0.0473323 0.0528938i
\(497\) −249.729 −0.502473
\(498\) −34.1782 + 185.203i −0.0686309 + 0.371894i
\(499\) 84.0984 84.0984i 0.168534 0.168534i −0.617801 0.786335i \(-0.711976\pi\)
0.786335 + 0.617801i \(0.211976\pi\)
\(500\) 173.508 + 388.100i 0.347017 + 0.776200i
\(501\) −118.213 + 118.213i −0.235953 + 0.235953i
\(502\) 529.005 + 768.442i 1.05380 + 1.53076i
\(503\) 327.870 0.651829 0.325914 0.945399i \(-0.394328\pi\)
0.325914 + 0.945399i \(0.394328\pi\)
\(504\) −71.7435 + 117.683i −0.142348 + 0.233497i
\(505\) 54.7909i 0.108497i
\(506\) −223.693 324.940i −0.442081 0.642174i
\(507\) −244.623 244.623i −0.482490 0.482490i
\(508\) −52.6692 + 137.841i −0.103680 + 0.271340i
\(509\) 34.6224 + 34.6224i 0.0680205 + 0.0680205i 0.740299 0.672278i \(-0.234684\pi\)
−0.672278 + 0.740299i \(0.734684\pi\)
\(510\) −29.7662 + 161.296i −0.0583651 + 0.316266i
\(511\) 424.963i 0.831630i
\(512\) −36.6407 + 510.687i −0.0715639 + 0.997436i
\(513\) −159.420 −0.310760
\(514\) 46.5661 + 8.59351i 0.0905954 + 0.0167189i
\(515\) −167.956 + 167.956i −0.326128 + 0.326128i
\(516\) −196.231 74.9804i −0.380294 0.145311i
\(517\) −428.184 + 428.184i −0.828210 + 0.828210i
\(518\) −370.548 + 255.090i −0.715343 + 0.492451i
\(519\) 113.430 0.218555
\(520\) −315.217 192.167i −0.606187 0.369553i
\(521\) 235.719i 0.452436i −0.974077 0.226218i \(-0.927364\pi\)
0.974077 0.226218i \(-0.0726362\pi\)
\(522\) 10.5245 7.24518i 0.0201618 0.0138797i
\(523\) −185.851 185.851i −0.355356 0.355356i 0.506742 0.862098i \(-0.330850\pi\)
−0.862098 + 0.506742i \(0.830850\pi\)
\(524\) −208.706 + 93.3063i −0.398294 + 0.178066i
\(525\) 135.216 + 135.216i 0.257555 + 0.257555i
\(526\) 479.610 + 88.5093i 0.911805 + 0.168269i
\(527\) 43.3524i 0.0822626i
\(528\) 163.423 + 146.240i 0.309514 + 0.276970i
\(529\) 92.2900 0.174461
\(530\) −69.7139 + 377.762i −0.131536 + 0.712759i
\(531\) −144.012 + 144.012i −0.271209 + 0.271209i
\(532\) 643.394 287.643i 1.20939 0.540683i
\(533\) 696.732 696.732i 1.30719 1.30719i
\(534\) 104.075 + 151.182i 0.194898 + 0.283111i
\(535\) 53.2408 0.0995155
\(536\) 697.572 169.174i 1.30144 0.315623i
\(537\) 229.135i 0.426695i
\(538\) 375.765 + 545.843i 0.698448 + 1.01458i
\(539\) 89.6428 + 89.6428i 0.166313 + 0.166313i
\(540\) 46.6590 + 17.8285i 0.0864055 + 0.0330157i
\(541\) −315.952 315.952i −0.584015 0.584015i 0.351989 0.936004i \(-0.385506\pi\)
−0.936004 + 0.351989i \(0.885506\pi\)
\(542\) 11.2348 60.8786i 0.0207284 0.112322i
\(543\) 283.676i 0.522424i
\(544\) 385.728 + 498.711i 0.709058 + 0.916749i
\(545\) 287.841 0.528149
\(546\) −375.663 69.3266i −0.688028 0.126972i
\(547\) −550.957 + 550.957i −1.00723 + 1.00723i −0.00725954 + 0.999974i \(0.502311\pi\)
−0.999974 + 0.00725954i \(0.997689\pi\)
\(548\) 361.929 947.204i 0.660454 1.72847i
\(549\) −154.676 + 154.676i −0.281741 + 0.281741i
\(550\) 250.620 172.530i 0.455673 0.313691i
\(551\) −65.3350 −0.118575
\(552\) −335.651 + 81.4013i −0.608063 + 0.147466i
\(553\) 23.6982i 0.0428539i
\(554\) −96.5631 + 66.4753i −0.174302 + 0.119992i
\(555\) 115.281 + 115.281i 0.207714 + 0.207714i
\(556\) 156.551 + 350.170i 0.281566 + 0.629802i
\(557\) 2.35545 + 2.35545i 0.00422882 + 0.00422882i 0.709218 0.704989i \(-0.249048\pi\)
−0.704989 + 0.709218i \(0.749048\pi\)
\(558\) −12.9830 2.39594i −0.0232670 0.00429379i
\(559\) 582.233i 1.04156i
\(560\) −220.476 + 12.2342i −0.393708 + 0.0218468i
\(561\) 270.048 0.481368
\(562\) 33.8994 183.692i 0.0603192 0.326855i
\(563\) 269.210 269.210i 0.478170 0.478170i −0.426376 0.904546i \(-0.640210\pi\)
0.904546 + 0.426376i \(0.140210\pi\)
\(564\) 216.378 + 483.991i 0.383650 + 0.858140i
\(565\) 108.507 108.507i 0.192047 0.192047i
\(566\) 64.3106 + 93.4187i 0.113623 + 0.165051i
\(567\) 51.6852 0.0911556
\(568\) 297.039 + 181.085i 0.522956 + 0.318812i
\(569\) 342.558i 0.602035i 0.953619 + 0.301018i \(0.0973263\pi\)
−0.953619 + 0.301018i \(0.902674\pi\)
\(570\) −144.827 210.379i −0.254083 0.369086i
\(571\) 153.948 + 153.948i 0.269610 + 0.269610i 0.828943 0.559333i \(-0.188943\pi\)
−0.559333 + 0.828943i \(0.688943\pi\)
\(572\) −216.953 + 567.787i −0.379288 + 0.992634i
\(573\) −43.2291 43.2291i −0.0754435 0.0754435i
\(574\) 106.957 579.570i 0.186335 1.00970i
\(575\) 479.190i 0.833373i
\(576\) 170.670 87.9539i 0.296301 0.152698i
\(577\) 563.693 0.976938 0.488469 0.872581i \(-0.337556\pi\)
0.488469 + 0.872581i \(0.337556\pi\)
\(578\) 195.071 + 35.9992i 0.337493 + 0.0622824i
\(579\) 446.223 446.223i 0.770678 0.770678i
\(580\) 19.1222 + 7.30664i 0.0329693 + 0.0125977i
\(581\) −220.769 + 220.769i −0.379981 + 0.379981i
\(582\) −65.9148 + 45.3766i −0.113256 + 0.0779666i
\(583\) 632.465 1.08484
\(584\) −308.152 + 505.469i −0.527657 + 0.865530i
\(585\) 138.441i 0.236651i
\(586\) 329.253 226.662i 0.561866 0.386796i
\(587\) 176.603 + 176.603i 0.300857 + 0.300857i 0.841349 0.540492i \(-0.181762\pi\)
−0.540492 + 0.841349i \(0.681762\pi\)
\(588\) 101.326 45.3000i 0.172324 0.0770409i
\(589\) 47.7355 + 47.7355i 0.0810450 + 0.0810450i
\(590\) −320.876 59.2159i −0.543857 0.100366i
\(591\) 319.858i 0.541215i
\(592\) 625.718 34.7210i 1.05696 0.0586504i
\(593\) −996.597 −1.68060 −0.840301 0.542120i \(-0.817622\pi\)
−0.840301 + 0.542120i \(0.817622\pi\)
\(594\) 14.9246 80.8726i 0.0251256 0.136149i
\(595\) −192.271 + 192.271i −0.323144 + 0.323144i
\(596\) −226.885 + 101.434i −0.380679 + 0.170191i
\(597\) 15.6147 15.6147i 0.0261553 0.0261553i
\(598\) −542.808 788.493i −0.907707 1.31855i
\(599\) −854.031 −1.42576 −0.712880 0.701286i \(-0.752610\pi\)
−0.712880 + 0.701286i \(0.752610\pi\)
\(600\) −62.7834 258.881i −0.104639 0.431469i
\(601\) 345.733i 0.575263i 0.957741 + 0.287631i \(0.0928678\pi\)
−0.957741 + 0.287631i \(0.907132\pi\)
\(602\) −197.473 286.853i −0.328028 0.476499i
\(603\) −190.334 190.334i −0.315645 0.315645i
\(604\) −833.557 318.504i −1.38006 0.527325i
\(605\) −99.2029 99.2029i −0.163972 0.163972i
\(606\) −14.3331 + 77.6677i −0.0236521 + 0.128165i
\(607\) 526.354i 0.867141i −0.901120 0.433570i \(-0.857254\pi\)
0.901120 0.433570i \(-0.142746\pi\)
\(608\) −973.859 124.407i −1.60174 0.204617i
\(609\) 21.1821 0.0347818
\(610\) −344.636 63.6007i −0.564977 0.104263i
\(611\) −1039.02 + 1039.02i −1.70053 + 1.70053i
\(612\) 84.3890 220.855i 0.137891 0.360874i
\(613\) 410.567 410.567i 0.669767 0.669767i −0.287895 0.957662i \(-0.592955\pi\)
0.957662 + 0.287895i \(0.0929554\pi\)
\(614\) −665.256 + 457.971i −1.08348 + 0.745881i
\(615\) −213.585 −0.347293
\(616\) 85.6859 + 353.318i 0.139100 + 0.573568i
\(617\) 514.755i 0.834287i −0.908841 0.417144i \(-0.863031\pi\)
0.908841 0.417144i \(-0.136969\pi\)
\(618\) 282.019 194.146i 0.456342 0.314152i
\(619\) 314.214 + 314.214i 0.507615 + 0.507615i 0.913794 0.406179i \(-0.133139\pi\)
−0.406179 + 0.913794i \(0.633139\pi\)
\(620\) −8.63278 19.3096i −0.0139238 0.0311446i
\(621\) 91.5828 + 91.5828i 0.147476 + 0.147476i
\(622\) −718.772 132.645i −1.15558 0.213256i
\(623\) 304.276i 0.488404i
\(624\) 396.560 + 354.863i 0.635512 + 0.568691i
\(625\) −225.209 −0.360334
\(626\) 167.509 907.690i 0.267586 1.44998i
\(627\) −297.350 + 297.350i −0.474243 + 0.474243i
\(628\) −182.054 407.215i −0.289895 0.648431i
\(629\) 545.669 545.669i 0.867518 0.867518i
\(630\) 46.9542 + 68.2064i 0.0745304 + 0.108264i
\(631\) −230.081 −0.364629 −0.182315 0.983240i \(-0.558359\pi\)
−0.182315 + 0.983240i \(0.558359\pi\)
\(632\) 17.1842 28.1877i 0.0271902 0.0446008i
\(633\) 21.0533i 0.0332596i
\(634\) −511.967 743.692i −0.807519 1.17302i
\(635\) 62.6875 + 62.6875i 0.0987205 + 0.0987205i
\(636\) 197.643 517.252i 0.310760 0.813290i
\(637\) 217.526 + 217.526i 0.341484 + 0.341484i
\(638\) 6.11654 33.1440i 0.00958705 0.0519498i
\(639\) 130.457i 0.204158i
\(640\) 271.116 + 145.321i 0.423618 + 0.227065i
\(641\) 746.825 1.16509 0.582547 0.812797i \(-0.302056\pi\)
0.582547 + 0.812797i \(0.302056\pi\)
\(642\) −75.4705 13.9277i −0.117555 0.0216942i
\(643\) 548.092 548.092i 0.852398 0.852398i −0.138030 0.990428i \(-0.544077\pi\)
0.990428 + 0.138030i \(0.0440772\pi\)
\(644\) −534.858 204.370i −0.830524 0.317345i
\(645\) −89.2426 + 89.2426i −0.138361 + 0.138361i
\(646\) −995.803 + 685.523i −1.54149 + 1.06118i
\(647\) 1055.00 1.63060 0.815302 0.579036i \(-0.196571\pi\)
0.815302 + 0.579036i \(0.196571\pi\)
\(648\) −61.4766 37.4783i −0.0948714 0.0578369i
\(649\) 537.223i 0.827771i
\(650\) 608.150 418.658i 0.935616 0.644090i
\(651\) −15.4762 15.4762i −0.0237730 0.0237730i
\(652\) 269.794 120.617i 0.413794 0.184995i
\(653\) −854.888 854.888i −1.30917 1.30917i −0.922015 0.387155i \(-0.873458\pi\)
−0.387155 0.922015i \(-0.626542\pi\)
\(654\) −408.024 75.2985i −0.623889 0.115135i
\(655\) 137.350i 0.209694i
\(656\) −547.480 + 611.809i −0.834574 + 0.932636i
\(657\) 221.998 0.337896
\(658\) −159.502 + 864.302i −0.242405 + 1.31353i
\(659\) −768.766 + 768.766i −1.16656 + 1.16656i −0.183556 + 0.983009i \(0.558761\pi\)
−0.983009 + 0.183556i \(0.941239\pi\)
\(660\) 120.282 53.7746i 0.182246 0.0814767i
\(661\) 312.323 312.323i 0.472500 0.472500i −0.430223 0.902723i \(-0.641565\pi\)
0.902723 + 0.430223i \(0.141565\pi\)
\(662\) −137.587 199.861i −0.207835 0.301904i
\(663\) 655.292 0.988374
\(664\) 422.678 102.507i 0.636563 0.154378i
\(665\) 423.420i 0.636721i
\(666\) −133.257 193.572i −0.200086 0.290648i
\(667\) 37.5333 + 37.5333i 0.0562719 + 0.0562719i
\(668\) 360.649 + 137.805i 0.539894 + 0.206295i
\(669\) 61.9610 + 61.9610i 0.0926173 + 0.0926173i
\(670\) 78.2626 424.085i 0.116810 0.632963i
\(671\) 577.004i 0.859916i
\(672\) 315.733 + 40.3337i 0.469840 + 0.0600204i
\(673\) 740.565 1.10039 0.550197 0.835035i \(-0.314553\pi\)
0.550197 + 0.835035i \(0.314553\pi\)
\(674\) 507.936 + 93.7367i 0.753614 + 0.139075i
\(675\) −70.6362 + 70.6362i −0.104646 + 0.104646i
\(676\) −285.166 + 746.308i −0.421843 + 1.10401i
\(677\) −547.118 + 547.118i −0.808151 + 0.808151i −0.984354 0.176203i \(-0.943619\pi\)
0.176203 + 0.984354i \(0.443619\pi\)
\(678\) −182.197 + 125.427i −0.268727 + 0.184995i
\(679\) −132.664 −0.195381
\(680\) 368.115 89.2746i 0.541346 0.131286i
\(681\) 77.6918i 0.114085i
\(682\) −28.6848 + 19.7470i −0.0420598 + 0.0289545i
\(683\) −407.623 407.623i −0.596813 0.596813i 0.342650 0.939463i \(-0.388676\pi\)
−0.939463 + 0.342650i \(0.888676\pi\)
\(684\) 150.263 + 336.105i 0.219682 + 0.491381i
\(685\) −430.772 430.772i −0.628864 0.628864i
\(686\) 734.396 + 135.529i 1.07055 + 0.197564i
\(687\) 415.987i 0.605513i
\(688\) 26.8786 + 484.388i 0.0390678 + 0.704052i
\(689\) 1534.73 2.22747
\(690\) −37.6576 + 204.057i −0.0545763 + 0.295735i
\(691\) 17.6037 17.6037i 0.0254757 0.0254757i −0.694254 0.719730i \(-0.744266\pi\)
0.719730 + 0.694254i \(0.244266\pi\)
\(692\) −106.915 239.144i −0.154501 0.345584i
\(693\) 96.4033 96.4033i 0.139110 0.139110i
\(694\) 44.4640 + 64.5892i 0.0640692 + 0.0930680i
\(695\) 230.448 0.331579
\(696\) −25.1949 15.3597i −0.0361996 0.0220685i
\(697\) 1010.98i 1.45047i
\(698\) 514.973 + 748.058i 0.737783 + 1.07172i
\(699\) −444.682 444.682i −0.636169 0.636169i
\(700\) 157.627 412.526i 0.225181 0.589323i
\(701\) 164.273 + 164.273i 0.234341 + 0.234341i 0.814502 0.580161i \(-0.197010\pi\)
−0.580161 + 0.814502i \(0.697010\pi\)
\(702\) 36.2157 196.244i 0.0515893 0.279550i
\(703\) 1201.68i 1.70935i
\(704\) 154.281 482.385i 0.219150 0.685205i
\(705\) 318.516 0.451795
\(706\) −474.710 87.6051i −0.672394 0.124087i
\(707\) −92.5829 + 92.5829i −0.130952 + 0.130952i
\(708\) 439.361 + 167.881i 0.620566 + 0.237119i
\(709\) 422.796 422.796i 0.596327 0.596327i −0.343006 0.939333i \(-0.611445\pi\)
0.939333 + 0.343006i \(0.111445\pi\)
\(710\) 172.157 118.515i 0.242475 0.166923i
\(711\) −12.3798 −0.0174118
\(712\) 220.638 361.919i 0.309886 0.508313i
\(713\) 54.8457i 0.0769224i
\(714\) 322.847 222.252i 0.452166 0.311277i
\(715\) 258.220 + 258.220i 0.361146 + 0.361146i
\(716\) −483.085 + 215.973i −0.674699 + 0.301639i
\(717\) 33.8375 + 33.8375i 0.0471932 + 0.0471932i
\(718\) −715.559 132.052i −0.996601 0.183917i
\(719\) 1029.00i 1.43115i −0.698534 0.715577i \(-0.746164\pi\)
0.698534 0.715577i \(-0.253836\pi\)
\(720\) −6.39107 115.175i −0.00887649 0.159966i
\(721\) 567.607 0.787250
\(722\) 210.621 1141.30i 0.291719 1.58075i
\(723\) −450.855 + 450.855i −0.623589 + 0.623589i
\(724\) −598.074 + 267.381i −0.826068 + 0.369311i
\(725\) −28.9488 + 28.9488i −0.0399293 + 0.0399293i
\(726\) 114.672 + 166.574i 0.157950 + 0.229441i
\(727\) −475.001 −0.653372 −0.326686 0.945133i \(-0.605932\pi\)
−0.326686 + 0.945133i \(0.605932\pi\)
\(728\) 207.924 + 857.354i 0.285609 + 1.17768i
\(729\) 27.0000i 0.0370370i
\(730\) 201.677 + 292.960i 0.276270 + 0.401314i
\(731\) 422.419 + 422.419i 0.577865 + 0.577865i
\(732\) 471.894 + 180.312i 0.644664 + 0.246328i
\(733\) −344.939 344.939i −0.470586 0.470586i 0.431519 0.902104i \(-0.357978\pi\)
−0.902104 + 0.431519i \(0.857978\pi\)
\(734\) −149.322 + 809.141i −0.203437 + 1.10237i
\(735\) 66.6831i 0.0907253i
\(736\) 487.989 + 630.926i 0.663028 + 0.857237i
\(737\) −710.021 −0.963393
\(738\) 302.764 + 55.8734i 0.410249 + 0.0757092i
\(739\) 363.340 363.340i 0.491665 0.491665i −0.417166 0.908831i \(-0.636976\pi\)
0.908831 + 0.417166i \(0.136976\pi\)
\(740\) 134.388 351.706i 0.181605 0.475278i
\(741\) −721.544 + 721.544i −0.973744 + 0.973744i
\(742\) 756.123 520.525i 1.01903 0.701516i
\(743\) 271.667 0.365636 0.182818 0.983147i \(-0.441478\pi\)
0.182818 + 0.983147i \(0.441478\pi\)
\(744\) 7.18588 + 29.6303i 0.00965843 + 0.0398257i
\(745\) 149.314i 0.200421i
\(746\) −525.771 + 361.948i −0.704787 + 0.485185i
\(747\) −115.328 115.328i −0.154389 0.154389i
\(748\) −254.536 569.340i −0.340288 0.761150i
\(749\) −89.9637 89.9637i −0.120112 0.120112i
\(750\) −362.051 66.8145i −0.482735 0.0890860i
\(751\) 1105.27i 1.47173i −0.677128 0.735866i \(-0.736776\pi\)
0.677128 0.735866i \(-0.263224\pi\)
\(752\) 816.447 912.380i 1.08570 1.21327i
\(753\) −807.937 −1.07296
\(754\) 14.8423 80.4265i 0.0196847 0.106666i
\(755\) −379.087 + 379.087i −0.502102 + 0.502102i
\(756\) −48.7163 108.968i −0.0644396 0.144137i
\(757\) 554.565 554.565i 0.732583 0.732583i −0.238548 0.971131i \(-0.576671\pi\)
0.971131 + 0.238548i \(0.0766713\pi\)
\(758\) −252.091 366.191i −0.332573 0.483102i
\(759\) 341.641 0.450119
\(760\) −307.033 + 503.634i −0.403990 + 0.662676i
\(761\) 188.496i 0.247695i 0.992301 + 0.123847i \(0.0395234\pi\)
−0.992301 + 0.123847i \(0.960477\pi\)
\(762\) −72.4626 105.260i −0.0950952 0.138137i
\(763\) −486.380 486.380i −0.637457 0.637457i
\(764\) −50.3939 + 131.886i −0.0659605 + 0.172625i
\(765\) −100.441 100.441i −0.131295 0.131295i
\(766\) −255.290 + 1383.35i −0.333277 + 1.80594i
\(767\) 1303.62i 1.69963i
\(768\) −346.299 276.921i −0.450910 0.360574i
\(769\) −593.354 −0.771592 −0.385796 0.922584i \(-0.626073\pi\)
−0.385796 + 0.922584i \(0.626073\pi\)
\(770\) 214.798 + 39.6397i 0.278958 + 0.0514801i
\(771\) −28.9973 + 28.9973i −0.0376100 + 0.0376100i
\(772\) −1361.36 520.179i −1.76342 0.673807i
\(773\) 514.720 514.720i 0.665873 0.665873i −0.290885 0.956758i \(-0.593950\pi\)
0.956758 + 0.290885i \(0.0939498\pi\)